Under some of the explored \(2\times 2\)  games, there were alternatives to the way the fixation probability of a single mutant depended on population size \(N\) . One common pattern found in these functions across anti-coordination games and the fixation of dominating strategies showed an initial plunge for small population sizes until a global minimum of the fixation probability \(\rho _N\)  was reached. We called \(N_{min}\)  to the population size under which this happened. This was followed by a steady increase up to a finite asymptotic value which can be computed following [1]}.
